Abstract
Rapid-equilibrium and compulsory-order cases are not exclusive in giving rise to a reciprocally bilinear initial rate behaviour in the generalized ternary-complex mechanism for enzymatic two-substrate reactions shown in Scheme 1. General expressions ▪ relating empirical Dalziel coefficients to velocity and equilibrium constants in Scheme 1 are derived and show that rapid-equilibrium and compulsory-order equations may be considered as opposite extremes of a general empirical Dalziel rate equation for the random-order ternary-complex mechanism. Kinetic characteristics of non-equilibrium ternary-complex mechanisms are described and discussed in view of the special case for which the second-degree rate equation corresponding to Scheme 1 becomes mathematically identical with a bilinear Dalziel equation. Kinetic differences between the bilinear special cases inherent in Scheme 1 primarily concern the Dalziel coefficients ϕ 1 and ϕ 2. Empirical Dalziel coefficients obtained for enzymes operating by this mechanism should always be interpreted in view of the general Dalziel equation, and any reduction of this relationship to those previously derived for rapid-equilibrium and compulsory-order cases must be supported by experimental evidence. General criteria imposing previously not recognized restrictions on the quotients ϕ 1/ ϕ 12 and ϕ 2/ ϕ 12 in comparison to equilibrium constants for the
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